In the designing stage in manufacturing, there is a need for determining optimal design parameters with respect to the design condition. For example, in the designing of an SRAM (static random access memory), as illustrated in FIG. 22 for example, the design values of the size (the area: W×L), Vth (the operation threshold of transistors included in the SRAM), leak current, power supply voltage, etc. are calculated in the initial of the designing.
In this case, when the yield rate is selected as the design condition for example, the designer performs the optimal design of the SRAM by comprehending the relation and the like of the yield rate and the size as well as other design values. Conventionally, such comprehension has often been determined by the knowledge/experience of the designer. However, as manufacturing system becomes more complicated, there has been a need for techniques to support the optimal design.
In the conventional design support techniques in the manufacturing design, as illustrated in FIG. 23 for example, design parameters are sampled in a design parameter space (S2301). These represent a design parameter combination for calculating the size, Vth, Leak, power supply voltage and so on. Next, a sample of each parameter combination is input into a simulator that simulates the operation of the design target (SRAM, for example), and a numerical calculation is performed (step S2302). Accordingly, the numerical calculation of the design condition such as the yield rate of the design target, as well as the design values of the size, Vth, Leak, supply voltage is performed. At this time, the numerical calculation of a plurality of objective functions (cost functions) for which the input is the design parameter combination for calculating the yield rate, for example, is performed. The relation between the numerically-calculated objective functions is then plotted on a display screen and the like (step S2303). The designer decides whether or not the accuracy of the part where the plurality of objective functions become optimal at the same time (called “Pareto frontier”) on the plotting screen is sufficient (step S2304). When the designer determines that the accuracy is not sufficient, the sampling is repeated further, and the numerical calculation by the simulator is performed repeatedly until the accuracy becomes sufficient.
However, in the conventional numerical calculation method as described above, when there are a large number of design parameter combinations and a large number of types of design parameters constituting each combination, if an attempt is made to search the search space thoroughly, a combinational explosion occurs, making it impossible to do the calculation within the real time.
Particularly, when the relation between a plurality of objective functions for calculating the yield rate or the relation between the objective functions and the size, Vth, Leak, power supply voltage needs to be visually recognized, conventionally, a significant amount of simulator calculation had to be done again every time a display axis (objective functions, design values, design parameters and so on) to be the comparison target is selected.
As described above, conventionally, there has been a problem that a large amount of time is required for the numerical calculation by the simulator, making it impossible to appropriately determine the accuracy of the Pareto frontier in the entire search area in the sampling, and making it difficult to realize the support for the optimal design.
For example, as illustrated in FIG. 24A-FIG. 24B, a case of calculating given objective functions f1(x1, x2) and f2(x1, x2) from design parameters x1, x2, and minimizing the values of the both objective functions at the same time is considered. In this case, in the initial stage of the designing, in the design parameter space (x1, x2) illustrated in FIG. 24A, sampling is performed evenly in the entire area, and the plotting in the objective function space (f1(x1, x2), f2(x1, x2)) illustrated in FIG. 24B is performed. At this stage, since it is difficult to predict the Pareto frontier, the sampling needs to be performed in as wide an area as possible, and the simulator calculation for that also requires a large amount of time.
Next, in the plotting in the objective function space, if the designer determines that the area 2501 in FIG. 25B is the optimal Pareto area, additional sampling is performed further around an area 2502, which is corresponding to the area 2501, in the design parameter space. In this case, the simulator calculation requires a large amount of time as well.